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Hindawi Publishing CorporationAdvances in Power ElectronicsVolume 2013 Article ID 719847 10 pageshttpdxdoiorg1011552013719847

Research ArticleDevelopment of a New Research Platform for Electrical DriveSystem Modelling for Real-Time Digital Simulation Applications

S Umashankar1 Mandar Bhalekar1 Surabhi Chandra1

D Vijayakumar1 and D P Kothari2

1 School of Electrical Engineering VIT University Vellore 632014 India2MVSR Engineering College Nadergul Hyderabad 501510 India

Correspondence should be addressed to S Umashankar shankarumsgmailcom

Received 31 January 2013 Revised 1 June 2013 Accepted 29 June 2013

Academic Editor Don Mahinda Vilathgamuwa

Copyright copy 2013 S Umashankar et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper presents the research platform for real-time digital simulation applications which replaces the requirement for full-scaleor partial-scale validation of physical systems To illustrate this a three-phaseAC-DC-AC converter topology has been used consistsof diode rectifier DC link and an IGBT inverter with inductive load In this topology rectifier as well as inverter decoupled andsolved separately using decoupled method which results in the reduced order system so that it is easy to solve the state equationThis method utilizes an analytical approach to formulate the state equations and interpolation methods have been implemented torectify the zero-crossing errors with fixed step size of 100 120583sec is usedThe proposed algorithm and the model have been validatedusing MATLAB simulation as m-file program and also in real-time DSP controller domain The performance of the real-timesystem model is evaluated based on accuracy zero crossing and step size

1 Introduction

The ever growing complexity and size of electric drives andtheir related mechanical loads [1] represent an importantchallenge for those responsible for their testing and verifi-cation The considerations highlight the need for a thoroughand exhaustive testing of the controls under conditions thatare realistic [2] For these reasons it is customary thatall controllers for high-power electric drives be tested incontrolled laboratory conditions [2]

A recent alternative way of testing that is fast becomingquite popular is to use fully real-time digital simulationThesesimulations can also be interfaced with industrial controllersthus saving a lot of the investment cost and allowing aneconomic tool for drive controller testing and offering theflexibility needed to simulate machines in all power ranges[2]Theuse of virtual system enables relatively easier interfaceof the drive systems to the computer and it allows fasterldquoonline data and signal processing for analysis purposesrdquoEarlier hardware has been replaced by equivalent simulationmodel and the same has been tested using controller the

so-called HIL Recently systems tested in real time fullydigital simulation with controller as well as hardware usinga simulation model [3]

Simulating a drive in real time starts with the problem ofmodelling the drive and various works have been made indeveloping models of drives most notably those in [1 2 4]The authors of [4] have proposed an interesting alternative tomodelling the drives using a state-spacemodel that can easilybe implemented using MATLAB and the parameters can befound from standard theories and tests [4] Many researchersare doing this research work and found various approximateand optimistic solution approach methods and tested thesame Based on their past experience a simple method toform state equations involves switching function method [5]This method involves mathematical modelling of a systemrather than a circuit-basedmodeling and hence does not havethe problemsmentioned like in PSpice PSIM [5ndash7] Also thismethod is defined by its function related to its state ratherthan its generalized equation But coupled method suffersfrom numerical error due to higher order system equationsSo in this work decoupled method is used which is very

2 Advances in Power Electronics

sim

Inductionmotor

sim

sim

IREC IINV

IDC

Vdc

Vsa

VsbVsc

D1 T D2 T D3 T

D1 B D2 B D3 B

TU1 TU2 TU3

TL1 TL2 TL3

Du1 Du2 Du3

Dl1 Dl2 Dl3

Figure 1 Three-phase converter topology with diode rectifier DC link and inverter fed IM

simVdc

sim

sim

D1 T D2 T D3 T

D1 B D2 B D3 B

Vsa

Vsb

Vsc

(a)

+minus

+minus

Inductionmotor

Vdc2

0

Vdc2

TU1 TU2 TU3

TL1 TL2 TL3

Du1 Du2 Du3

Dl1 Dl2 Dl3

(b)

Figure 2 (a) Circuit 1 diode rectifier with DC link (b) Circuit 2 inverter fed induction motor with DC source

simple and allows developing the analytical equations suitablefor any power electronic system by decoupling rectifier andinverter This also gives exact solution and error is almostreduced

In this paper decoupled method for a simple three-phaseDC link inverter fed induction machine is proposed Thetopology of the converter considered in this paper comprisesdiode rectifier capacitive DC link PWM IGBT inverterand induction motor as load Decoupled analytical methodis used to solve all the state variables of the earlier testcircuit (source current DC link voltage and load current)for accurate results Decoupling is implemented to reducethe system equation order so as to achieve fast calculationand easier to get an analytical expression from solution tostate-space equations of the two converters Performanceparameters of the drive system have been validated usingMATLAB scripts (m-file) and also on DSP platform Thismethod has advantages like reduced system order simplifiedsolution easier calculation exact zero crossing and less datastorage due to large step size comparing coupled method

2 Methodology

Figure 1 represents the topology of the power converter tobe modelled with decoupled algorithm with zero crossingIn every sampling period of the discrete model two circuitsare considered The first part of the circuit consists of an AC

voltage source having an internal impedance connected to adiode rectifier with a DC link capacitor The second part ishaving a constant voltage source in DC link PWM inverterand an IM load At the end of every sampling period DC linkvoltage is computed by integrating the difference in rectifierand inverter currents

The proposed decoupled algorithm to solve the state-space equation of the electric drive system is given later

Step 1 Initialization parameters of the selected system

Step 2 Decouple the diode bridge rectifier and inverter fedinduction motor circuit

Step 3 Define different cases with an equivalent circuit fortwo decoupled circuits

Step 4 Assume that 119881dc0 is a known value (initial value = 0)

Step 5 Solve state-space equation of the diode bridgerectifier and find rectifier side DC link current (119868REC)

using analyticalnumerical method based on its switchingstatesfunction

Step 6 Solve state-space equation of inverter fed induc-tion motor and find inverter side DC links current (119868INV)

using analyticalnumerical method based on its switchingstatesfunction (see Figure 2)

Advances in Power Electronics 3

PU

Va

Vb

Vc

+minus

+minus

0Vdc2

Vdc2

N

sim

sim

sim

Ea

Eb

Ec

Lla

Llb

Llc

Rla

Rlb

Rlc

PL

TU1 TU2 TU3Du1 Du2 Du3

TL1 TL2 TL3Dl1 Dl2 Dl3

Figure 3 IGBT-diode inverter circuit with equivalent inductionmotor

Step 7 Find capacitor current 119868DC119899+1

using rectifier andinverter side DC link currents from Steps 5 and 6 respec-tively

Step 8 Solve the differential equation of DC link current andfind 119881DC

119899+1

using analyticalnumerical method

Step 9 Repeat the iteration for all cases up to stop time

Step 10 Compare with offline simulation results usingSimulinkSimulation tool

119868REC119899+1

= ((05 lowast (1 + sign (119868119886119904119899+1

) lowast 119868119886119904119899+1

)

+ (05 lowast (1 + sign (119868119887119904119899+1

)) lowast 119868119887119904119899+1

)

+ (05 lowast (1 + sign (119868119888119904119899+1

)) lowast 119868119888119904119899+1

)))

(1)

119868INV119899+1

= 05 lowast ((1198681198791198801

+ 1198681198631198801

) minus (1198681198791198711

+ 1198681198631198711

)

+ (1198681198791198802

+ 1198681198631198802

) minus (1198681198791198712

+ 1198681198631198712

)

+ (1198681198791198803

+ 1198681198631198803

) minus (1198681198791198713

+ 1198681198631198713

))

(2)

The equation for diode rectifier side DC link currentcomponent is obtained by using individual diode currentsshown in (1) where 119868IREC

119899+1

is rectifier side DC component ofcurrent at 119899 + 1 sample and 119868

1198861199041 1198681198871199041 and 119868

1198881199041are (119899 + 1)th

sample of source side currents of Phase (119886) (119887) and (119888)respectively in Inverter

The equation for inverter side DC link current compo-nent is obtained by using individual switch currents anddiode currents shown in (2) where 119868INV

119899+1

is inverter sideDC Component of DC link current at (119899 + 1)th sample1198681198791198801

1198681198791198802

and 1198681198791198803

are 119899th sample of upper switch cur-rents and 119868

1198791198711 1198681198791198712

and 1198681198791198713

are (119899 + 1)th sample of lowerswitch currents of phases (119886) (119887) and (119888) respectively inInverter

119868DC119899+1

= 119868REC119899+1

minus 119868INV119899+1

(3)

0 002 004 006 008 01

0

50

100

150

Time (s)

Curr

ent (

A)

minus50

minus100

II A Phase source REF

Diode rectifier source current Ts = 1120583s decoupled Ts = 100120583s

I A Phase source RTDS

Figure 4 Diode rectifier side source current in phase A for bothREF (blue trace) and RTDS (red traces)

0 002 004 006 008 010

50

100

150

200

250

300

350

400

450Vo

ltage

s (V

)

Time (s)

DC link voltage and its PLECS Ref Ts = 1120583s RTS Ts = 100120583s

Vdc link-RTDSVdc link-Ref

Figure 5 DC link voltage REF (blue trace) RTDS (red trace)

where 119868DC119899+1

is capacitor current at 119899 + 1 sampleFrom (3) DC link voltage of (119899 + 1)th sample can be

calculated as

119881DC119899+1

= 119881DC119899

+ (ℎ

119862dc) lowast 119868DC

119899+1

(4)

This sample is used to formulate the four different casesand its switching logic for an inverter circuit explainedin Section 3 for identifying all these parameters for nextiteration or time step

3 Modelling of IGBT-Diode Inverter andInduction Machine

Consider the IGBT-diode inverter circuit as in Figure 3 withinduction machine load Assume that two DC link voltages


are equal (119881dc2 each) Then voltage at the DC link midpointis at zero potential Similarly Ea Eb and Ec are considered tobe back emf of induction machine in each phase and ldquo119873rdquo isthe neutral point of the induction machine stator windingsLet us assume that 119881

1198860 1198811198870 and 119881

1198880are the pole voltages of

each phase legConsider only that phases leg A and P

119880 P119871are the PWM

pulses to upper (T1198801) and lower (T

1198711) IGBT switches If

we define modes of operation for the phase leg A aloneby considering its state variables and PWM sequenceswe arrive at four different examples as given in whatfollows

Case 1 (119875119880

= 1 119875119871

= 0) upper IGBT switches on condition

(((05 sdot 119881dc minus 119864119909) gt 0) ampamp ((119875

119906minus 119875119897) == 1)

100381710038171003817100381710038171003817((119868 lt 0)ampamp((119877119868 + 119871 (

119868 minus 119868119863119906

119867) + 119864119909

+ 119881119873119874

) gt 05119881dc))

119868119879119880

=(1 + sign (119868))

2lowast 119875119880

119868 119868119863119880

=(1 minus sign (119868))

2lowast (1 minus 119875

119871) 119868

119881119909119900

= (119875119906

minus 119875119871) sdot

119881dc2

(5)

Case 2 (119875119880

= 0 119875119871

= 1) lower IGBT switches on condition

(((minus05 sdot 119881dc minus 119864119909) gt 0)ampamp ((119875

119906minus 119875119897) == minus1)

100381710038171003817100381710038171003817((119868 gt 0)ampamp((119877119868 + 119871 (

119868 minus 119868119863119906

119867) + 119864119909

+ 119881119873119874

) gt minus05119881dc))

119868119879119871

=(1 minus sign (119868))

2lowast 119875119871119868 119868

119879119880=

(1 + sign (119868))


119880) 119868

119881119909119900

= (119875119906

minus 119875119871) sdot

119881dc2

(6)

Case 3 (119875119880

= 1 119875119871

= 1) shorted leg mode

119868119909119899+1

= 119868119909119899exp(minus

119905

119879) (7)

Case 4 (119875119880

= 0 119875119871

= 0) diode bridge mode IGBT switchesoff conditionCase 41 If

((119864119909

+ 119881119873119874

) gt 05119881dc)

119868119863119880

= 119868

119868119879119880

= 0

119881119909119900

=119881dc2

(8)

Case 42 If

((119864119909

+ 119881119873119874

) gt minus05119881dc)

119868119863119880

= 119868

119868119879119880

= 0

119881119909119900

= minus119881dc2

(9)

Case 43 If

(1003816100381610038161003816119864119909 + 119881

119873119874

1003816100381610038161003816 lt 05119881dc)ampamp119868 = 0

119868119863119880

= 0

119868119879119880

= 0

119881119909119900

= 0

(10)

where 119875119880is PWMpulse to upper switch 119875

119871is PWMpulse to

lower switch 119909 are phases (119886) (119887) and (119888) and 119868 is inductionmachine current in (119886) (119887) and (119888) reference frames


001 002 003 004 005 006 007 008 009 01

0

100

200

300

DC link two-level (IGBT-diode) inverter

minus100

minus200

minus300

V PhA to neutral RTDSV PhA to neutral REF

Time (s)

Van

(V)

Figure 6 Inverter phase A neutral (Van) voltage REF (blue trace)RTDS (red traces)

002 004 006 008 01 012 014 016 018 02

0

10

20

30

40

50

60

Torq

ue (N

m)


Torque RTDSTorque REF

Time (s)

Applied torque T load

Figure 7 Torque developed REF (blue trace) RTDS (red trace)

The logic for two IGBT switches in phase ldquo119886rdquo is given inwhat follows based on the conditions given previously as perfour different cases

1198791199061198861

= (((Sign (1198681199041198860

) = 1)1003817100381710038171003817 (1198681199041198860

= 0))ampamp

(((05 lowast 119881dc0 minus 11988111989911989900

) ge 0)ampamp

(1198751199061198861

minus 1198751198971198861

) = 1))

1198791198971198861

= (((Sign (1198681199041198860

) = minus1)1003817100381710038171003817 (1198681199041198860

= 0))ampamp

(((minus05 lowast 119881dc0 minus 11988111989911989900

) le 0)ampamp

(1198751199061198861

minus 1198751198971198861

) = minus1))

(11)

Similar logic for other two phases (119887) and (119888) is obtainedby replacing the subscript ldquo119886rdquo in earlier two equations by ldquo119887rdquoand ldquo119888rdquo Switching logic for the diode is explained in detail in[8] and hence has not been given here Similarly switchingfunction logic for IGBT-diode combination from individualIGBT logic and Diode logic is given later for all the switchesin upper legs and lower legs

Phase leg A top switches on (either IGBT or diode)

1198781199061198861

= 1198791199061198861

1003817100381710038171003817 1198631199061198861

1198781198971198861

= 1198791198971198861

1003817100381710038171003817 1198631198971198861

(12)

Phase leg B top switches on (either IGBT or diode)

1198781199061198871

= 1198791199061198871

1003817100381710038171003817 1198631199061198871

1198781198971198871

= 1198791198971198871

1003817100381710038171003817 1198631198971198871

(13)

Phase leg C top switches on (either IGBT or diode)

1198781199061198881

= 1198791199061198881

1003817100381710038171003817 1198631199061198881

1198781198971198881

= 1198791198971198881

1003817100381710038171003817 1198631198971198881

(14)

Phase to DC link midpoint voltage is given by

11988111988601

= 05 lowast 119881dc0 lowast (1198781199061198861

minus 1198781198971198861

)

11988111988701

= 05 lowast 119881dc0 lowast (1198781199061198871

minus 1198781198971198871

)

11988111988801

= 05 lowast 119881dc0 lowast (1198781199061198881

minus 1198781198971198881

)

(15)

Machine side of each phase voltage is given by

1198811198861198991

= (1

3) lowast (2 lowast 119881

11988601minus 11988111988701

minus 11988111988801

)

1198811198871198991

= (1

3) lowast (minus119881

11988601+ 2 lowast 119881

11988701minus 11988111988801

)

1198811198881198991

= (1


11988601minus 11988111988701

+ 2 lowast 11988111988801

)

(16)

Voltages 1198811198861198991

1198811198871198991

and 1198811198881198991

in the previously equationare used as an input stator voltage for induction motor Inorder to find the various electrical and mechanical parame-ters like speed flux and current through stator terminals asimplified or reduced order model has to be developed whichhas been explained in detail later

While modelling induction machine the order of thesystem plays an important role in real-time simulation [9]In general induction machine is modelled in two-phasereference frame Sometimes this leads to more state matrixparameters and more computation time At the same timeif it is modelled as the lowest order system then the state


variables may deviate from its actual values this leads to pooraccuracy and instability In order to compromise betweenaccuracy and computation time the induction machine ismodelled in stationary two-phase reference frame (120572-120573)

which satisfies the previous criteria This model has advan-tages like fewer matrix parameters calculation preservationof symmetry of the induction machine model state matrixand minimization of computation time [9 10]

Induction machine model in 120572-120573 reference frame is asfollows

119889

119889119905119883 (119905) = [119860

119888(120596)] 119883 (119905) + [119861

119888] 119880 (119905)

119884 (119905) = [119862119888] 119883 (119905)

(17)

where the input vector [U(t)] is chosen to be the reference120572-120573 stator voltages [X(t)] is the 120572-120573 stator and rotor fluxstate vector (input) [Y(t)] is the 120572-120573 stator and rotor currentoutput vector (output) and [119860

119888(120596)] [119861

119888] and [119862

119888] are state

matrix input matrix and output matrix respectivelyAs per the reference from [9 10] induction machine

equation in 120572-120573 is expressed in complete form as shown inwhat follows

119889

119889119905

[[[[[

[

120593119904120572

120593119904120573

120593119903120572

120593119903120573

]]]]]

]

=

[[[[[[[[[

[

minus119877119904

1205901198711199040

(1 minus 120590) 119877119904

120590119872119904119903

0

0minus119877119904

1205901198711199040

(1 minus 120590) 119877119904

120590119872119904119903

(1 minus 120590)

120590119872119904119903

119877119903 0minus119877119903

120590119871119903minus119901120596

0(1 minus 120590)

120590119872119904119903

119877119903 119901120596minus119877119903

120590119871119903

]]]]]]]]]

]

times

[[[[[

[

120593119904120572

120593119904120573

120593119903120572

120593119903120573

]]]]]

]

+

[[[[[

[

1 0

0 1

0 0

0 0

]]]]]

]

[V119904120572

V119904120573

]

[[[

[

119894119904120572

119894119904120573

119894119903120572

119894119903120573

]]]

]

=

[[[[[[[[[[[

[

1

1205901198711199040

minus (1 minus 120590)

120590119872119904119903

0

01

1205901198711199040


120590119872119904119903


120590119872119904119903

01

120590119871119903minus119901120596

0minus (1 minus 120590)

120590119872119904119903

1199011205961

120590119871119903

]]]]]]]]]]]

]

times[[[

[

120593119904120572

120593119904120573

120593119903120572

120593119903120573

]]]

]

002 004 006 008 01 012 014 016 018 02

0

20

40

60

80

100

120

140


Speed radianss RTDSSpeed radianss REF

minus20

Time (s)

Wm

(rad

s)

Figure 8 Rotor speed in rads REF (blue trace) RTDS (red trace)

002 004 006 008 01 012 014 016 018 02

0

10

20

30

40

50

IL-p

hA (A

)DC link two-level (IGBT-diode) inverter

IL-phaseA RTDSIL-phaseA REF

Time (s)

minus10

minus20

minus30

minus40

Figure 9 Stator ph-A current REF (blue trace) RTDS (red trace)

[[[

[

119894119904120572

119894119904120573

120593119903120572

120593119903120573

]]]

]

119899+1

=[[[

[

11989211 11989212 11989213 11989214

11989221 11989222 11989223 11989224

11989231 11989232 11989233 11989234

11989241 11989242 11989243 11989244

]]]

]

times[[[

[

119894119904120572

119894119904120573

120593119903120572

120593119903120573

]]]

]

119899

+[[[

[

ℎ11 ℎ12

ℎ21 ℎ22

ℎ31 ℎ32

ℎ41 ℎ42

]]]

]

[119881119904120572

119881119904120573

]

119899

(18)

where 120590 = 1minus(1198722

119904119903119871119904119871119903) p = no of pole pairs in a machine

and 120596 = speed in rads


002 004 006 008 01 012 014 016 018 02

0

50

100

150

EMF

phas

e A (V


EMF phase A RTDS

minus50

minus100

minus150

Time (s)

Figure 10 Stator ph-A back EMF-REF (blue trace) RTDS (redtrace)

Three-phaseinverter Load

PWM pulses MATLABCode

composerstudio

UncontrolledrectifierAC power

input

DSP1

DSP2

IGBT inverter module-1 IGBT inverter

module-2

RTDS

DSP1

DSP2

UART

DC linkvoltage AC power

output

Figure 11 Block diagram and snapshot of hardware setup

In order to find back emf set 119894119904120572

= 0 and 119894119904120573

= 0 Then119864119904120572

= 119881119904120572 119864119904120573

= 119881119904120573

[119864119904120572

119864119904120573

]

119899

=minus1

(ℎ11 sdot ℎ22 minus ℎ21 sdot ℎ12)[

ℎ22 minusℎ12

minusℎ21 ℎ11]

times [11989213 11989214

11989223 11989224] [

120593119903120572

120593119903120573

]

119899

(19)

ePWM3

WAWB

C280xC28x3xePWM

ePWM2

WAWB

C280xC28x3x

ePWM

ePWM1

WA

WB

C280xC28x3x

ePWM

Sine wave3

Sine wave2

Sine wave1

F28335 eZdsp

Data type conversion2

Uint16


Uint16

Data type conversion

Uint16

Figure 12 DSP interface for PWM pulse generation

Table 1 Input parameters for RTDS and Simulink-PLECS

Source parameters DC link inverter Load parametersVm = 1414 lowast 220119891 = 50120596 = 2 lowast pi lowast 119891Rs = 1Ω

Ls = 10mH

Cdc = 10mFFsw = 450Hz119867 = 100119890 minus 6 s

119898 = 08

As given in Table 3

where g119898119899 h119898119899

are the state and input matrix coefficients ofthe stationary reference frame model of induction machineAt every sampling time stator currents have been calculatedusing stator voltages and finally back emf of each phasehas been calculated as per (19) Current sample of back emfhas been used for the next iteration to identify the mode ofoperation of inverter given in Section 3With these equationsa generalized model of the complete electrical drive systemhas been developed and validated with offline Simulink-PLECS model given later

4 Simulation Results

Input parameters for proposedmodel as well as for Simulink-PLECS (REF) offline simulation are shown in Table 1

41 Offline Results versus Real-Time Digital Simulator Inthis case simulations are carried out with both rectifier andinverter now decoupled at DC link Both circuits are treatedas separate circuits and rectifier current with DC link andinverter current with DC link are calculated separately At theend of the iteration DC link voltage will be updated using therectifier and inverter currents

In Figures 4 5 6 7 8 9 and 10 red trace is fromSimulink-PLECS reference results which are overplotted onthat of RTDS-decoupled solution From Figures 4ndash10 it isvery clear that proposed real-timemodel and offline Simulinkresults are matching each other in terms of accuracy as wellas with larger step size of 100120583119904 proposedmodel with the 1120583119904

Simulink reference modelTable 2 shows that at a particular time of sample electrical

and mechanical parameters of real-time electrical drive


10050

0minus50

minus100018 0185 019 0195 02 0205 021 0215 022 0225

Time (s)

Input phase-phase voltage

Phas

e-ph

ase

volta

ge (V

)

2010

0minus10minus20

Input current (R-phase)

Inpu

t R-p

hase

curr

ent (

A)

018 0185 019 0195 02 0205 021 0215 022 0225Time (s)

(a)

80604020

002 0202 0204 0206 0208 021 0212 0214 0216 0218 022

Time (s)

DC

link

(V)

DC link voltage

201510

50

minus5

DC

link

curr

ent (

A)

02 0202 0204 0206 0208 021 0212 0214 0216 0218 022Time (s)

DC link current

(b)

105

0019 0195 02 0205 021 0215 022 0225 023 0235

Time (s)

Gat

e pul

se (V

) Gate pulses for leg 1

Gate pulses for leg 2


019 0195 02 0205 021 0215 022 0225 023 0235Time (s)

019 0195 02 0205 021 0215 022 0225 023 0235Time (s)

Gat

e pul

se (V

)

105

0

105

0

Gat

e pul

se (V

)

(c)

10050

0minus50

minus10002 0205 021 0215 022 0225 023 0235 024 0245

Time (s)

AC output voltagePh

ase-

phas

evo

ltage

(V)

3210

minus1minus2minus3

R-ph

ase c

urre

nt (A

) AC output current (R-phase)

02 0205 021 0215 022 0225 023 0235 024 0245Time (s)

(d)

Figure 13 Proposed mathematical model offline results showing (a) input voltage (ph-ph) and current (R-phase) (b) DC link voltage andcurrent (c) PWM pulses for 3 legs of inverter and (d) output voltage (ph-ph) and current (R-Phase)

Table 2 Comparison of proposed real-time digital simulator results with Simulink-PLECS offline results

S no Parameter Time of sampleReferenceSimulink-PLECS(119886)

Proposed RTDSsolution

(119887)

Percentage of error ()((119887) minus (119886))(119886)

1 DC link voltage V 001 8546 8588 04910102 5001 5009 01

2 Rectifier source current in phase A Amps 0008 1215 1214 minus00820086 2418 2471 219

3 Stator current in phase A Amps 0009512 5195 518 minus000288008951 5596 555 minus000822

4 Inverter line to neutral voltage van (V) 0009512 3333 3333 0008951 3333 3333 0

5 Electromagnetic torque tem (N-m) 001186 6633 6686 0701985 2202 2202 00

6 Rotor speed 120596 (rads) 002 3141 3171 0901922 14848 14851 002


(a) (b)

(c) (d)

Figure 14 Hardware results from DSP showing (a) input voltage (ph-ph) and current (R-Phase) (b) DC link voltage and current (c) PWMpulses for 3 legs of inverter from DSP and (d) output voltage (ph-ph) and current (R-phase)

systemmodel utilizingAC-DC-AC topology listed previouslyare closelymatchedwith its Simulink reference offline results

5 Real-Time Implementation Using DSP

The given system model is implemented in MATLAB m-file coding and also in real-time hardware setup using theDSP-MATLAB interface PWM are pulses for hardware andMATLAB model generated using DSP processor 2 ePWMmodule is used to generate six pulses at a time from ePWMpins of DSP These pulses are being fed to optocoupler TLP250 which boosts up the voltage level to an extent at whichIGBT switches can be triggered At the same time anotherprocessor is used to run the mathematical model of drivesystem as per decoupled method

Figure 11 represents the block diagram of the hard-ware setup As per specifications given in Appendix A twoSemikron make IGBT IPM module-based inverters used forthis purpose one acts as a rectifier and the other is used as aninverter to drive inductionmotor Pulses fromDSP2 are givento the Semikron inverter module 2 through the optoisolatorICs in order to strengthen the gate drive signal The PWMlogic is developed in Simulink model and Figure 12 showsthe logic generation of bipolar PWM for three-phase inverterComparative results are obtained for the input ph-ph voltageof diode rectifier and input phase current as shown in Figures13(a) and 14(a) Figures 13(b) and 14(b) show DC link voltageand current waveforms

The PWM pulses generated at the output of the optoiso-lator are shown in Figure 14(c) and those from the simulationare shown in Figure 13(c) In Figure 14 all voltage waveformsare phase-phase voltages with the multiplier setting of 200and all current waveforms are phase A current waveforms

with the probe setting at 10mVA Figures 13 and 14(d)reveal that the output voltage between two phases and phasecurrents is closely matched with that of the offline simulationresults As per analytical calculations as well as simulationand hardware results the output RMS voltage obtained acrossthe load is 85V All the parameters are matched except forthe grid voltage and current since it has been assumed as theideal source in simulation model and real grid conditions inthe laboratory are ignored But in practical situations the gridcould be connected to transformers and many other loads inthe laboratory building

6 Conclusion

A new research platform for power electronics and drivesystem modelling using decoupled analytical method hasbeen verified both in offline simulation and in real-timehardware The m-file program developed for state-spacemethod-based electrical drive model accurately matchingwith hardware model The same model has been validatedusing eZdsp processors with one as plant and the other asa controller Decoupled method makes it easier with betteraccuracy and less calculation time which results in fastexecution speed This can be further extended to test thesame with reduced order induction motor model and resultscan be compared with existing results in order to furtherimprovise the real-time model accuracy and its executiontime The results obtained from this work suggest that thedeveloped models using the proposed method can be usedas a research platform and extended to any complex powerelectronic applications The obtained model is flexible andit can be extended to any system with different size (systemorder) These models can be used as user definedfunction


Table 3 Load specification three-phase induction motor

Parameter Value DescriptionkVAbase 4e3 Rated kVA of the machineVbase 400 Rated voltage (L-L) in (V)Vm 231 lowast radic2 Peak value of AC source voltage (V)119891 50 Rated frequency in Hz120596 2 lowast pi lowast 50 Rated angular frequency in radsRs 1405 Stator resistance in Ω

Ls(Lls + Lm) 0178039 Stator inductance in HRr 1395 Rotor resistance in Ω

Lr(Llr + Lm) 0178039 Rotor inductance in HLm 01722 Stator-rotor mutual inductance in Hℎ 100 Time step in 120583s119899 9 Carrier frequency 119899 times 50Hz119869 00131 Inertia of the machine in kgm2

119861 001841 Friction coefficient in Nmsrad119901 2 No of pole pairs

blocks to test with real-time processorcontroller for futureresearch work

Appendices

A Three-Phase IGBT-Based Inverter(Semikron Make)

IGBT module used SKM75GB123DDC link capacitor 4700 120583FGate driver SKYPER 32 PRO119881dc input 800 (V)119881ac output 415 (V)119868ac output 20 (A)Output frequency 50HzSwitching frequency 10 kHzType of cooling force air cooledTemp 35∘CDuty class class I

B

For more details see Table 3

References

[1] P Livinti and R Pusca ldquoControl of an electric drive system inthe LabVIEWprogramming environmentrdquo inProceedings of the9th International Conference on Remote Engineering and VirtualInstrumentation (REV) pp 1ndash6 Bilbao Spain July 2012

[2] R Champagne L A Dessaint andH Fortin-Blanchette ldquoReal-time simulation of electric drivesrdquoMathematics and Computersin Simulation vol 63 no 3-5 pp 173ndash181 2003

[3] H Eren and C C Fung ldquoVirtual instrumentation of electricdrive systems for automation and testingrdquo in Proceedings ofthe 17th IEEE Instrumentation and Measurement TechnologyConference (IMTC rsquo00) vol 3 pp 1500ndash1505 May 2000

[4] R Champagne L Dessaint G Sybille and B KhodabakhchianldquoApproach for real-time simulation of electric drivesrdquo in Pro-ceedings of the Canadian Conference on Electrical and ComputerEgineering (CCECE rsquo00) vol 1 pp 340ndash344 May 2000

[5] C Bordas C Dufour and O Rudloff ldquoA 3-level neutral-clamped inverter model with natural switching mode sup-port for the real-time simulation of variable speed drivesrdquoin Proceedings of the International Symposium on AdvancedElectromechanical Motion Systems pp 1ndash8 Lille France 2009

[6] A Myaing and V Dinavahi ldquoFPGA-based real-time emulationof power electronic systems with detailed representation ofdevice characteristicsrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 1 pp 358ndash368 2011

[7] J H Allmeling and W P Hammer ldquoPLECSmdashpiece-wise linearelectrical circuit simulation for Simulinkrdquo in Proceedings of theIEEE International Conference on Power Electronics and DriveSystems (PEDSrsquo99) vol 1 pp 355ndash360 July 1999

[8] S Venugopal and G Narayanan ldquoDesign of FPGA based digitalplatform for control of power electronics systemsrdquo in Proceed-ings of the National Power Electronics Conference pp 1250ndash1255December 2005

[9] K Jayalakshmi and V Ramanarayanan ldquoReal-time simulationof electrical machines on FPGA platformrdquo in Proceedings of theIndia International Conference on Power Electronics (IICPE rsquo06)pp 259ndash263 Chennai India December 2006

[10] R Krishnan Electric Motor Drives Modeling Analysis andControl Pearson Education Asia 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



sim

Inductionmotor

sim

sim

IREC IINV

IDC

Vdc

Vsa

VsbVsc

D1 T D2 T D3 T

D1 B D2 B D3 B

TU1 TU2 TU3

TL1 TL2 TL3

Du1 Du2 Du3

Dl1 Dl2 Dl3

Figure 1 Three-phase converter topology with diode rectifier DC link and inverter fed IM

simVdc

sim

sim

D1 T D2 T D3 T

D1 B D2 B D3 B

Vsa

Vsb

Vsc

(a)

+minus

+minus

Inductionmotor

Vdc2

0

Vdc2

TU1 TU2 TU3

TL1 TL2 TL3

Du1 Du2 Du3

Dl1 Dl2 Dl3

(b)

Figure 2 (a) Circuit 1 diode rectifier with DC link (b) Circuit 2 inverter fed induction motor with DC source

simple and allows developing the analytical equations suitablefor any power electronic system by decoupling rectifier andinverter This also gives exact solution and error is almostreduced

In this paper decoupled method for a simple three-phaseDC link inverter fed induction machine is proposed Thetopology of the converter considered in this paper comprisesdiode rectifier capacitive DC link PWM IGBT inverterand induction motor as load Decoupled analytical methodis used to solve all the state variables of the earlier testcircuit (source current DC link voltage and load current)for accurate results Decoupling is implemented to reducethe system equation order so as to achieve fast calculationand easier to get an analytical expression from solution tostate-space equations of the two converters Performanceparameters of the drive system have been validated usingMATLAB scripts (m-file) and also on DSP platform Thismethod has advantages like reduced system order simplifiedsolution easier calculation exact zero crossing and less datastorage due to large step size comparing coupled method

2 Methodology

Figure 1 represents the topology of the power converter tobe modelled with decoupled algorithm with zero crossingIn every sampling period of the discrete model two circuitsare considered The first part of the circuit consists of an AC

voltage source having an internal impedance connected to adiode rectifier with a DC link capacitor The second part ishaving a constant voltage source in DC link PWM inverterand an IM load At the end of every sampling period DC linkvoltage is computed by integrating the difference in rectifierand inverter currents

The proposed decoupled algorithm to solve the state-space equation of the electric drive system is given later

Step 1 Initialization parameters of the selected system

Step 2 Decouple the diode bridge rectifier and inverter fedinduction motor circuit

Step 3 Define different cases with an equivalent circuit fortwo decoupled circuits

Step 4 Assume that 119881dc0 is a known value (initial value = 0)

Step 5 Solve state-space equation of the diode bridgerectifier and find rectifier side DC link current (119868REC)

using analyticalnumerical method based on its switchingstatesfunction

Step 6 Solve state-space equation of inverter fed induc-tion motor and find inverter side DC links current (119868INV)

using analyticalnumerical method based on its switchingstatesfunction (see Figure 2)


PU

Va

Vb

Vc

+minus

+minus

0Vdc2

Vdc2

N

sim

sim

sim

Ea

Eb

Ec

Lla

Llb

Llc

Rla

Rlb

Rlc

PL







119899+1




119868REC119899+1

= ((05 lowast (1 + sign (119868119886119904119899+1

) lowast 119868119886119904119899+1

)

+ (05 lowast (1 + sign (119868119887119904119899+1

)) lowast 119868119887119904119899+1

)

+ (05 lowast (1 + sign (119868119888119904119899+1

)) lowast 119868119888119904119899+1

)))

(1)

119868INV119899+1

= 05 lowast ((1198681198791198801

+ 1198681198631198801

) minus (1198681198791198711

+ 1198681198631198711

)

+ (1198681198791198802

+ 1198681198631198802

) minus (1198681198791198712

+ 1198681198631198712

)

+ (1198681198791198803

+ 1198681198631198803

) minus (1198681198791198713

+ 1198681198631198713

))

(2)


119899+1


1198861199041 1198681198871199041 and 119868

1198881199041are (119899 + 1)th



119899+1


1198681198791198802

and 1198681198791198803


1198791198711 1198681198791198712

and 1198681198791198713


119868DC119899+1

= 119868REC119899+1

minus 119868INV119899+1

(3)

0 002 004 006 008 01

0

50

100

150

Time (s)

Curr

ent (

A)

minus50

minus100





0 002 004 006 008 010

50

100

150

200

250

300

350

400

450Vo

ltage

s (V

)

Time (s)




where 119868DC119899+1


calculated as

119881DC119899+1

= 119881DC119899

+ (ℎ


119899+1

(4)






1198860 1198811198870 and 119881







Case 1 (119875119880

= 1 119875119871



119906minus 119875119897) == 1)

100381710038171003817100381710038171003817((119868 lt 0)ampamp((119877119868 + 119871 (

119868 minus 119868119863119906

119867) + 119864119909

+ 119881119873119874

) gt 05119881dc))

119868119879119880

=(1 + sign (119868))

2lowast 119875119880

119868 119868119863119880

=(1 minus sign (119868))


119871) 119868

119881119909119900

= (119875119906

minus 119875119871) sdot

119881dc2

(5)

Case 2 (119875119880

= 0 119875119871



119906minus 119875119897) == minus1)

100381710038171003817100381710038171003817((119868 gt 0)ampamp((119877119868 + 119871 (

119868 minus 119868119863119906

119867) + 119864119909

+ 119881119873119874


119868119879119871

=(1 minus sign (119868))

2lowast 119875119871119868 119868

119879119880=

(1 + sign (119868))


119880) 119868

119881119909119900

= (119875119906

minus 119875119871) sdot

119881dc2

(6)

Case 3 (119875119880

= 1 119875119871


119868119909119899+1

= 119868119909119899exp(minus

119905

119879) (7)

Case 4 (119875119880

= 0 119875119871


((119864119909

+ 119881119873119874

) gt 05119881dc)

119868119863119880

= 119868

119868119879119880

= 0

119881119909119900

=119881dc2

(8)

Case 42 If

((119864119909

+ 119881119873119874


119868119863119880

= 119868

119868119879119880

= 0

119881119909119900

= minus119881dc2

(9)

Case 43 If

(1003816100381610038161003816119864119909 + 119881

119873119874

1003816100381610038161003816 lt 05119881dc)ampamp119868 = 0

119868119863119880

= 0

119868119879119880

= 0

119881119909119900

= 0

(10)





001 002 003 004 005 006 007 008 009 01

0

100

200

300


minus100

minus200

minus300


Time (s)

Van

(V)


002 004 006 008 01 012 014 016 018 02

0

10

20

30

40

50

60

Torq

ue (N

m)



Time (s)




1198791199061198861

= (((Sign (1198681199041198860

) = 1)1003817100381710038171003817 (1198681199041198860

= 0))ampamp

(((05 lowast 119881dc0 minus 11988111989911989900

) ge 0)ampamp

(1198751199061198861

minus 1198751198971198861

) = 1))

1198791198971198861

= (((Sign (1198681199041198860

) = minus1)1003817100381710038171003817 (1198681199041198860

= 0))ampamp


) le 0)ampamp

(1198751199061198861

minus 1198751198971198861

) = minus1))

(11)



1198781199061198861

= 1198791199061198861

1003817100381710038171003817 1198631199061198861

1198781198971198861

= 1198791198971198861

1003817100381710038171003817 1198631198971198861

(12)


1198781199061198871

= 1198791199061198871

1003817100381710038171003817 1198631199061198871

1198781198971198871

= 1198791198971198871

1003817100381710038171003817 1198631198971198871

(13)


1198781199061198881

= 1198791199061198881

1003817100381710038171003817 1198631199061198881

1198781198971198881

= 1198791198971198881

1003817100381710038171003817 1198631198971198881

(14)


11988111988601

= 05 lowast 119881dc0 lowast (1198781199061198861

minus 1198781198971198861

)

11988111988701

= 05 lowast 119881dc0 lowast (1198781199061198871

minus 1198781198971198871

)

11988111988801

= 05 lowast 119881dc0 lowast (1198781199061198881

minus 1198781198971198881

)

(15)


1198811198861198991

= (1


11988601minus 11988111988701

minus 11988111988801

)

1198811198871198991

= (1


11988601+ 2 lowast 119881

11988701minus 11988111988801

)

1198811198881198991

= (1


11988601minus 11988111988701

+ 2 lowast 11988111988801

)

(16)

Voltages 1198811198861198991

1198811198871198991

and 1198811198881198991







119889

119889119905119883 (119905) = [119860

119888(120596)] 119883 (119905) + [119861

119888] 119880 (119905)

119884 (119905) = [119862119888] 119883 (119905)

(17)


119888(120596)] [119861

119888] and [119862

119888] are state



119889

119889119905

[[[[[

[

120593119904120572

120593119904120573

120593119903120572

120593119903120573

]]]]]

]

=

[[[[[[[[[

[

minus119877119904

1205901198711199040

(1 minus 120590) 119877119904

120590119872119904119903

0

0minus119877119904

1205901198711199040

(1 minus 120590) 119877119904

120590119872119904119903

(1 minus 120590)

120590119872119904119903

119877119903 0minus119877119903

120590119871119903minus119901120596

0(1 minus 120590)

120590119872119904119903

119877119903 119901120596minus119877119903

120590119871119903

]]]]]]]]]

]

times

[[[[[

[

120593119904120572

120593119904120573

120593119903120572

120593119903120573

]]]]]

]

+

[[[[[

[

1 0

0 1

0 0

0 0

]]]]]

]

[V119904120572

V119904120573

]

[[[

[

119894119904120572

119894119904120573

119894119903120572

119894119903120573

]]]

]

=

[[[[[[[[[[[

[

1

1205901198711199040


120590119872119904119903

0

01

1205901198711199040


120590119872119904119903


120590119872119904119903

01

120590119871119903minus119901120596


120590119872119904119903

1199011205961

120590119871119903

]]]]]]]]]]]

]

times[[[

[

120593119904120572

120593119904120573

120593119903120572

120593119903120573

]]]

]

002 004 006 008 01 012 014 016 018 02

0

20

40

60

80

100

120

140



minus20

Time (s)

Wm

(rad

s)


002 004 006 008 01 012 014 016 018 02

0

10

20

30

40

50

IL-p

hA (A



Time (s)

minus10

minus20

minus30

minus40


[[[

[

119894119904120572

119894119904120573

120593119903120572

120593119903120573

]]]

]

119899+1

=[[[

[

11989211 11989212 11989213 11989214

11989221 11989222 11989223 11989224

11989231 11989232 11989233 11989234

11989241 11989242 11989243 11989244

]]]

]

times[[[

[

119894119904120572

119894119904120573

120593119903120572

120593119903120573

]]]

]

119899

+[[[

[

ℎ11 ℎ12

ℎ21 ℎ22

ℎ31 ℎ32

ℎ41 ℎ42

]]]

]

[119881119904120572

119881119904120573

]

119899

(18)

where 120590 = 1minus(1198722




002 004 006 008 01 012 014 016 018 02

0

50

100

150

EMF

phas

e A (V


EMF phase A RTDS

minus50

minus100

minus150

Time (s)




composerstudio


input

DSP1

DSP2


module-2

RTDS

DSP1

DSP2

UART


output



= 0 and 119894119904120573

= 0 Then119864119904120572

= 119881119904120572 119864119904120573

= 119881119904120573

[119864119904120572

119864119904120573

]

119899

=minus1


ℎ22 minusℎ12

minusℎ21 ℎ11]

times [11989213 11989214

11989223 11989224] [

120593119903120572

120593119903120573

]

119899

(19)

ePWM3

WAWB

C280xC28x3xePWM

ePWM2

WAWB

C280xC28x3x

ePWM

ePWM1

WA

WB

C280xC28x3x

ePWM

Sine wave3

Sine wave2

Sine wave1

F28335 eZdsp


Uint16


Uint16


Uint16




Ls = 10mH


119898 = 08

As given in Table 3

where g119898119899 h119898119899









10050

0minus50

minus100018 0185 019 0195 02 0205 021 0215 022 0225

Time (s)


Phas

e-ph

ase

volta

ge (V

)

2010

0minus10minus20


Inpu

t R-p

hase

curr

ent (

A)

018 0185 019 0195 02 0205 021 0215 022 0225Time (s)

(a)

80604020

002 0202 0204 0206 0208 021 0212 0214 0216 0218 022

Time (s)

DC

link

(V)

DC link voltage

201510

50

minus5

DC

link

curr

ent (

A)

02 0202 0204 0206 0208 021 0212 0214 0216 0218 022Time (s)

DC link current

(b)

105

0019 0195 02 0205 021 0215 022 0225 023 0235

Time (s)

Gat

e pul

se (V




019 0195 02 0205 021 0215 022 0225 023 0235Time (s)

019 0195 02 0205 021 0215 022 0225 023 0235Time (s)

Gat

e pul

se (V

)

105

0

105

0

Gat

e pul

se (V

)

(c)

10050

0minus50

minus10002 0205 021 0215 022 0225 023 0235 024 0245

Time (s)

AC output voltagePh

ase-

phas

evo

ltage

(V)

3210

minus1minus2minus3

R-ph

ase c

urre

nt (A


02 0205 021 0215 022 0225 023 0235 024 0245Time (s)

(d)





(119887)


1 DC link voltage V 001 8546 8588 04910102 5001 5009 01





6 Rotor speed 120596 (rads) 002 3141 3171 0901922 14848 14851 002


(a) (b)

(c) (d)








6 Conclusion









Appendices



B


References













RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










PU

Va

Vb

Vc

+minus

+minus

0Vdc2

Vdc2

N

sim

sim

sim

Ea

Eb

Ec

Lla

Llb

Llc

Rla

Rlb

Rlc

PL







119899+1




119868REC119899+1

= ((05 lowast (1 + sign (119868119886119904119899+1

) lowast 119868119886119904119899+1

)

+ (05 lowast (1 + sign (119868119887119904119899+1

)) lowast 119868119887119904119899+1

)

+ (05 lowast (1 + sign (119868119888119904119899+1

)) lowast 119868119888119904119899+1

)))

(1)

119868INV119899+1

= 05 lowast ((1198681198791198801

+ 1198681198631198801

) minus (1198681198791198711

+ 1198681198631198711

)

+ (1198681198791198802

+ 1198681198631198802

) minus (1198681198791198712

+ 1198681198631198712

)

+ (1198681198791198803

+ 1198681198631198803

) minus (1198681198791198713

+ 1198681198631198713

))

(2)


119899+1


1198861199041 1198681198871199041 and 119868

1198881199041are (119899 + 1)th



119899+1


1198681198791198802

and 1198681198791198803


1198791198711 1198681198791198712

and 1198681198791198713


119868DC119899+1

= 119868REC119899+1

minus 119868INV119899+1

(3)

0 002 004 006 008 01

0

50

100

150

Time (s)

Curr

ent (

A)

minus50

minus100





0 002 004 006 008 010

50

100

150

200

250

300

350

400

450Vo

ltage

s (V

)

Time (s)




where 119868DC119899+1


calculated as

119881DC119899+1

= 119881DC119899

+ (ℎ


119899+1

(4)






1198860 1198811198870 and 119881







Case 1 (119875119880

= 1 119875119871



119906minus 119875119897) == 1)

100381710038171003817100381710038171003817((119868 lt 0)ampamp((119877119868 + 119871 (

119868 minus 119868119863119906

119867) + 119864119909

+ 119881119873119874

) gt 05119881dc))

119868119879119880

=(1 + sign (119868))

2lowast 119875119880

119868 119868119863119880

=(1 minus sign (119868))


119871) 119868

119881119909119900

= (119875119906

minus 119875119871) sdot

119881dc2

(5)

Case 2 (119875119880

= 0 119875119871



119906minus 119875119897) == minus1)

100381710038171003817100381710038171003817((119868 gt 0)ampamp((119877119868 + 119871 (

119868 minus 119868119863119906

119867) + 119864119909

+ 119881119873119874


119868119879119871

=(1 minus sign (119868))

2lowast 119875119871119868 119868

119879119880=

(1 + sign (119868))


119880) 119868

119881119909119900

= (119875119906

minus 119875119871) sdot

119881dc2

(6)

Case 3 (119875119880

= 1 119875119871


119868119909119899+1

= 119868119909119899exp(minus

119905

119879) (7)

Case 4 (119875119880

= 0 119875119871


((119864119909

+ 119881119873119874

) gt 05119881dc)

119868119863119880

= 119868

119868119879119880

= 0

119881119909119900

=119881dc2

(8)

Case 42 If

((119864119909

+ 119881119873119874


119868119863119880

= 119868

119868119879119880

= 0

119881119909119900

= minus119881dc2

(9)

Case 43 If

(1003816100381610038161003816119864119909 + 119881

119873119874

1003816100381610038161003816 lt 05119881dc)ampamp119868 = 0

119868119863119880

= 0

119868119879119880

= 0

119881119909119900

= 0

(10)





001 002 003 004 005 006 007 008 009 01

0

100

200

300


minus100

minus200

minus300


Time (s)

Van

(V)


002 004 006 008 01 012 014 016 018 02

0

10

20

30

40

50

60

Torq

ue (N

m)



Time (s)




1198791199061198861

= (((Sign (1198681199041198860

) = 1)1003817100381710038171003817 (1198681199041198860

= 0))ampamp

(((05 lowast 119881dc0 minus 11988111989911989900

) ge 0)ampamp

(1198751199061198861

minus 1198751198971198861

) = 1))

1198791198971198861

= (((Sign (1198681199041198860

) = minus1)1003817100381710038171003817 (1198681199041198860

= 0))ampamp


) le 0)ampamp

(1198751199061198861

minus 1198751198971198861

) = minus1))

(11)



1198781199061198861

= 1198791199061198861

1003817100381710038171003817 1198631199061198861

1198781198971198861

= 1198791198971198861

1003817100381710038171003817 1198631198971198861

(12)


1198781199061198871

= 1198791199061198871

1003817100381710038171003817 1198631199061198871

1198781198971198871

= 1198791198971198871

1003817100381710038171003817 1198631198971198871

(13)


1198781199061198881

= 1198791199061198881

1003817100381710038171003817 1198631199061198881

1198781198971198881

= 1198791198971198881

1003817100381710038171003817 1198631198971198881

(14)


11988111988601

= 05 lowast 119881dc0 lowast (1198781199061198861

minus 1198781198971198861

)

11988111988701

= 05 lowast 119881dc0 lowast (1198781199061198871

minus 1198781198971198871

)

11988111988801

= 05 lowast 119881dc0 lowast (1198781199061198881

minus 1198781198971198881

)

(15)


1198811198861198991

= (1


11988601minus 11988111988701

minus 11988111988801

)

1198811198871198991

= (1


11988601+ 2 lowast 119881

11988701minus 11988111988801

)

1198811198881198991

= (1


11988601minus 11988111988701

+ 2 lowast 11988111988801

)

(16)

Voltages 1198811198861198991

1198811198871198991

and 1198811198881198991







119889

119889119905119883 (119905) = [119860

119888(120596)] 119883 (119905) + [119861

119888] 119880 (119905)

119884 (119905) = [119862119888] 119883 (119905)

(17)


119888(120596)] [119861

119888] and [119862

119888] are state



119889

119889119905

[[[[[

[

120593119904120572

120593119904120573

120593119903120572

120593119903120573

]]]]]

]

=

[[[[[[[[[

[

minus119877119904

1205901198711199040

(1 minus 120590) 119877119904

120590119872119904119903

0

0minus119877119904

1205901198711199040

(1 minus 120590) 119877119904

120590119872119904119903

(1 minus 120590)

120590119872119904119903

119877119903 0minus119877119903

120590119871119903minus119901120596

0(1 minus 120590)

120590119872119904119903

119877119903 119901120596minus119877119903

120590119871119903

]]]]]]]]]

]

times

[[[[[

[

120593119904120572

120593119904120573

120593119903120572

120593119903120573

]]]]]

]

+

[[[[[

[

1 0

0 1

0 0

0 0

]]]]]

]

[V119904120572

V119904120573

]

[[[

[

119894119904120572

119894119904120573

119894119903120572

119894119903120573

]]]

]

=

[[[[[[[[[[[

[

1

1205901198711199040


120590119872119904119903

0

01

1205901198711199040


120590119872119904119903


120590119872119904119903

01

120590119871119903minus119901120596


120590119872119904119903

1199011205961

120590119871119903

]]]]]]]]]]]

]

times[[[

[

120593119904120572

120593119904120573

120593119903120572

120593119903120573

]]]

]

002 004 006 008 01 012 014 016 018 02

0

20

40

60

80

100

120

140



minus20

Time (s)

Wm

(rad

s)


002 004 006 008 01 012 014 016 018 02

0

10

20

30

40

50

IL-p

hA (A



Time (s)

minus10

minus20

minus30

minus40


[[[

[

119894119904120572

119894119904120573

120593119903120572

120593119903120573

]]]

]

119899+1

=[[[

[

11989211 11989212 11989213 11989214

11989221 11989222 11989223 11989224

11989231 11989232 11989233 11989234

11989241 11989242 11989243 11989244

]]]

]

times[[[

[

119894119904120572

119894119904120573

120593119903120572

120593119903120573

]]]

]

119899

+[[[

[

ℎ11 ℎ12

ℎ21 ℎ22

ℎ31 ℎ32

ℎ41 ℎ42

]]]

]

[119881119904120572

119881119904120573

]

119899

(18)

where 120590 = 1minus(1198722




002 004 006 008 01 012 014 016 018 02

0

50

100

150

EMF

phas

e A (V


EMF phase A RTDS

minus50

minus100

minus150

Time (s)




composerstudio


input

DSP1

DSP2


module-2

RTDS

DSP1

DSP2

UART


output



= 0 and 119894119904120573

= 0 Then119864119904120572

= 119881119904120572 119864119904120573

= 119881119904120573

[119864119904120572

119864119904120573

]

119899

=minus1


ℎ22 minusℎ12

minusℎ21 ℎ11]

times [11989213 11989214

11989223 11989224] [

120593119903120572

120593119903120573

]

119899

(19)

ePWM3

WAWB

C280xC28x3xePWM

ePWM2

WAWB

C280xC28x3x

ePWM

ePWM1

WA

WB

C280xC28x3x

ePWM

Sine wave3

Sine wave2

Sine wave1

F28335 eZdsp


Uint16


Uint16


Uint16




Ls = 10mH


119898 = 08

As given in Table 3

where g119898119899 h119898119899









10050

0minus50

minus100018 0185 019 0195 02 0205 021 0215 022 0225

Time (s)


Phas

e-ph

ase

volta

ge (V

)

2010

0minus10minus20


Inpu

t R-p

hase

curr

ent (

A)

018 0185 019 0195 02 0205 021 0215 022 0225Time (s)

(a)

80604020

002 0202 0204 0206 0208 021 0212 0214 0216 0218 022

Time (s)

DC

link

(V)

DC link voltage

201510

50

minus5

DC

link

curr

ent (

A)

02 0202 0204 0206 0208 021 0212 0214 0216 0218 022Time (s)

DC link current

(b)

105

0019 0195 02 0205 021 0215 022 0225 023 0235

Time (s)

Gat

e pul

se (V




019 0195 02 0205 021 0215 022 0225 023 0235Time (s)

019 0195 02 0205 021 0215 022 0225 023 0235Time (s)

Gat

e pul

se (V

)

105

0

105

0

Gat

e pul

se (V

)

(c)

10050

0minus50

minus10002 0205 021 0215 022 0225 023 0235 024 0245

Time (s)

AC output voltagePh

ase-

phas

evo

ltage

(V)

3210

minus1minus2minus3

R-ph

ase c

urre

nt (A


02 0205 021 0215 022 0225 023 0235 024 0245Time (s)

(d)





(119887)


1 DC link voltage V 001 8546 8588 04910102 5001 5009 01





6 Rotor speed 120596 (rads) 002 3141 3171 0901922 14848 14851 002


(a) (b)

(c) (d)








6 Conclusion









Appendices



B


References













RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











1198860 1198811198870 and 119881







Case 1 (119875119880

= 1 119875119871



119906minus 119875119897) == 1)

100381710038171003817100381710038171003817((119868 lt 0)ampamp((119877119868 + 119871 (

119868 minus 119868119863119906

119867) + 119864119909

+ 119881119873119874

) gt 05119881dc))

119868119879119880

=(1 + sign (119868))

2lowast 119875119880

119868 119868119863119880

=(1 minus sign (119868))


119871) 119868

119881119909119900

= (119875119906

minus 119875119871) sdot

119881dc2

(5)

Case 2 (119875119880

= 0 119875119871



119906minus 119875119897) == minus1)

100381710038171003817100381710038171003817((119868 gt 0)ampamp((119877119868 + 119871 (

119868 minus 119868119863119906

119867) + 119864119909

+ 119881119873119874


119868119879119871

=(1 minus sign (119868))

2lowast 119875119871119868 119868

119879119880=

(1 + sign (119868))


119880) 119868

119881119909119900

= (119875119906

minus 119875119871) sdot

119881dc2

(6)

Case 3 (119875119880

= 1 119875119871


119868119909119899+1

= 119868119909119899exp(minus

119905

119879) (7)

Case 4 (119875119880

= 0 119875119871


((119864119909

+ 119881119873119874

) gt 05119881dc)

119868119863119880

= 119868

119868119879119880

= 0

119881119909119900

=119881dc2

(8)

Case 42 If

((119864119909

+ 119881119873119874


119868119863119880

= 119868

119868119879119880

= 0

119881119909119900

= minus119881dc2

(9)

Case 43 If

(1003816100381610038161003816119864119909 + 119881

119873119874

1003816100381610038161003816 lt 05119881dc)ampamp119868 = 0

119868119863119880

= 0

119868119879119880

= 0

119881119909119900

= 0

(10)





001 002 003 004 005 006 007 008 009 01

0

100

200

300


minus100

minus200

minus300


Time (s)

Van

(V)


002 004 006 008 01 012 014 016 018 02

0

10

20

30

40

50

60

Torq

ue (N

m)



Time (s)




1198791199061198861

= (((Sign (1198681199041198860

) = 1)1003817100381710038171003817 (1198681199041198860

= 0))ampamp

(((05 lowast 119881dc0 minus 11988111989911989900

) ge 0)ampamp

(1198751199061198861

minus 1198751198971198861

) = 1))

1198791198971198861

= (((Sign (1198681199041198860

) = minus1)1003817100381710038171003817 (1198681199041198860

= 0))ampamp


) le 0)ampamp

(1198751199061198861

minus 1198751198971198861

) = minus1))

(11)



1198781199061198861

= 1198791199061198861

1003817100381710038171003817 1198631199061198861

1198781198971198861

= 1198791198971198861

1003817100381710038171003817 1198631198971198861

(12)


1198781199061198871

= 1198791199061198871

1003817100381710038171003817 1198631199061198871

1198781198971198871

= 1198791198971198871

1003817100381710038171003817 1198631198971198871

(13)


1198781199061198881

= 1198791199061198881

1003817100381710038171003817 1198631199061198881

1198781198971198881

= 1198791198971198881

1003817100381710038171003817 1198631198971198881

(14)


11988111988601

= 05 lowast 119881dc0 lowast (1198781199061198861

minus 1198781198971198861

)

11988111988701

= 05 lowast 119881dc0 lowast (1198781199061198871

minus 1198781198971198871

)

11988111988801

= 05 lowast 119881dc0 lowast (1198781199061198881

minus 1198781198971198881

)

(15)


1198811198861198991

= (1


11988601minus 11988111988701

minus 11988111988801

)

1198811198871198991

= (1


11988601+ 2 lowast 119881

11988701minus 11988111988801

)

1198811198881198991

= (1


11988601minus 11988111988701

+ 2 lowast 11988111988801

)

(16)

Voltages 1198811198861198991

1198811198871198991

and 1198811198881198991







119889

119889119905119883 (119905) = [119860

119888(120596)] 119883 (119905) + [119861

119888] 119880 (119905)

119884 (119905) = [119862119888] 119883 (119905)

(17)


119888(120596)] [119861

119888] and [119862

119888] are state



119889

119889119905

[[[[[

[

120593119904120572

120593119904120573

120593119903120572

120593119903120573

]]]]]

]

=

[[[[[[[[[

[

minus119877119904

1205901198711199040

(1 minus 120590) 119877119904

120590119872119904119903

0

0minus119877119904

1205901198711199040

(1 minus 120590) 119877119904

120590119872119904119903

(1 minus 120590)

120590119872119904119903

119877119903 0minus119877119903

120590119871119903minus119901120596

0(1 minus 120590)

120590119872119904119903

119877119903 119901120596minus119877119903

120590119871119903

]]]]]]]]]

]

times

[[[[[

[

120593119904120572

120593119904120573

120593119903120572

120593119903120573

]]]]]

]

+

[[[[[

[

1 0

0 1

0 0

0 0

]]]]]

]

[V119904120572

V119904120573

]

[[[

[

119894119904120572

119894119904120573

119894119903120572

119894119903120573

]]]

]

=

[[[[[[[[[[[

[

1

1205901198711199040


120590119872119904119903

0

01

1205901198711199040


120590119872119904119903


120590119872119904119903

01

120590119871119903minus119901120596


120590119872119904119903

1199011205961

120590119871119903

]]]]]]]]]]]

]

times[[[

[

120593119904120572

120593119904120573

120593119903120572

120593119903120573

]]]

]

002 004 006 008 01 012 014 016 018 02

0

20

40

60

80

100

120

140



minus20

Time (s)

Wm

(rad

s)


002 004 006 008 01 012 014 016 018 02

0

10

20

30

40

50

IL-p

hA (A



Time (s)

minus10

minus20

minus30

minus40


[[[

[

119894119904120572

119894119904120573

120593119903120572

120593119903120573

]]]

]

119899+1

=[[[

[

11989211 11989212 11989213 11989214

11989221 11989222 11989223 11989224

11989231 11989232 11989233 11989234

11989241 11989242 11989243 11989244

]]]

]

times[[[

[

119894119904120572

119894119904120573

120593119903120572

120593119903120573

]]]

]

119899

+[[[

[

ℎ11 ℎ12

ℎ21 ℎ22

ℎ31 ℎ32

ℎ41 ℎ42

]]]

]

[119881119904120572

119881119904120573

]

119899

(18)

where 120590 = 1minus(1198722




002 004 006 008 01 012 014 016 018 02

0

50

100

150

EMF

phas

e A (V


EMF phase A RTDS

minus50

minus100

minus150

Time (s)




composerstudio


input

DSP1

DSP2


module-2

RTDS

DSP1

DSP2

UART


output



= 0 and 119894119904120573

= 0 Then119864119904120572

= 119881119904120572 119864119904120573

= 119881119904120573

[119864119904120572

119864119904120573

]

119899

=minus1


ℎ22 minusℎ12

minusℎ21 ℎ11]

times [11989213 11989214

11989223 11989224] [

120593119903120572

120593119903120573

]

119899

(19)

ePWM3

WAWB

C280xC28x3xePWM

ePWM2

WAWB

C280xC28x3x

ePWM

ePWM1

WA

WB

C280xC28x3x

ePWM

Sine wave3

Sine wave2

Sine wave1

F28335 eZdsp


Uint16


Uint16


Uint16




Ls = 10mH


119898 = 08

As given in Table 3

where g119898119899 h119898119899









10050

0minus50

minus100018 0185 019 0195 02 0205 021 0215 022 0225

Time (s)


Phas

e-ph

ase

volta

ge (V

)

2010

0minus10minus20


Inpu

t R-p

hase

curr

ent (

A)

018 0185 019 0195 02 0205 021 0215 022 0225Time (s)

(a)

80604020

002 0202 0204 0206 0208 021 0212 0214 0216 0218 022

Time (s)

DC

link

(V)

DC link voltage

201510

50

minus5

DC

link

curr

ent (

A)

02 0202 0204 0206 0208 021 0212 0214 0216 0218 022Time (s)

DC link current

(b)

105

0019 0195 02 0205 021 0215 022 0225 023 0235

Time (s)

Gat

e pul

se (V




019 0195 02 0205 021 0215 022 0225 023 0235Time (s)

019 0195 02 0205 021 0215 022 0225 023 0235Time (s)

Gat

e pul

se (V

)

105

0

105

0

Gat

e pul

se (V

)

(c)

10050

0minus50

minus10002 0205 021 0215 022 0225 023 0235 024 0245

Time (s)

AC output voltagePh

ase-

phas

evo

ltage

(V)

3210

minus1minus2minus3

R-ph

ase c

urre

nt (A


02 0205 021 0215 022 0225 023 0235 024 0245Time (s)

(d)





(119887)


1 DC link voltage V 001 8546 8588 04910102 5001 5009 01





6 Rotor speed 120596 (rads) 002 3141 3171 0901922 14848 14851 002


(a) (b)

(c) (d)








6 Conclusion









Appendices



B


References













RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










001 002 003 004 005 006 007 008 009 01

0

100

200

300


minus100

minus200

minus300


Time (s)

Van

(V)


002 004 006 008 01 012 014 016 018 02

0

10

20

30

40

50

60

Torq

ue (N

m)



Time (s)




1198791199061198861

= (((Sign (1198681199041198860

) = 1)1003817100381710038171003817 (1198681199041198860

= 0))ampamp

(((05 lowast 119881dc0 minus 11988111989911989900

) ge 0)ampamp

(1198751199061198861

minus 1198751198971198861

) = 1))

1198791198971198861

= (((Sign (1198681199041198860

) = minus1)1003817100381710038171003817 (1198681199041198860

= 0))ampamp


) le 0)ampamp

(1198751199061198861

minus 1198751198971198861

) = minus1))

(11)



1198781199061198861

= 1198791199061198861

1003817100381710038171003817 1198631199061198861

1198781198971198861

= 1198791198971198861

1003817100381710038171003817 1198631198971198861

(12)


1198781199061198871

= 1198791199061198871

1003817100381710038171003817 1198631199061198871

1198781198971198871

= 1198791198971198871

1003817100381710038171003817 1198631198971198871

(13)


1198781199061198881

= 1198791199061198881

1003817100381710038171003817 1198631199061198881

1198781198971198881

= 1198791198971198881

1003817100381710038171003817 1198631198971198881

(14)


11988111988601

= 05 lowast 119881dc0 lowast (1198781199061198861

minus 1198781198971198861

)

11988111988701

= 05 lowast 119881dc0 lowast (1198781199061198871

minus 1198781198971198871

)

11988111988801

= 05 lowast 119881dc0 lowast (1198781199061198881

minus 1198781198971198881

)

(15)


1198811198861198991

= (1


11988601minus 11988111988701

minus 11988111988801

)

1198811198871198991

= (1


11988601+ 2 lowast 119881

11988701minus 11988111988801

)

1198811198881198991

= (1


11988601minus 11988111988701

+ 2 lowast 11988111988801

)

(16)

Voltages 1198811198861198991

1198811198871198991

and 1198811198881198991







119889

119889119905119883 (119905) = [119860

119888(120596)] 119883 (119905) + [119861

119888] 119880 (119905)

119884 (119905) = [119862119888] 119883 (119905)

(17)


119888(120596)] [119861

119888] and [119862

119888] are state



119889

119889119905

[[[[[

[

120593119904120572

120593119904120573

120593119903120572

120593119903120573

]]]]]

]

=

[[[[[[[[[

[

minus119877119904

1205901198711199040

(1 minus 120590) 119877119904

120590119872119904119903

0

0minus119877119904

1205901198711199040

(1 minus 120590) 119877119904

120590119872119904119903

(1 minus 120590)

120590119872119904119903

119877119903 0minus119877119903

120590119871119903minus119901120596

0(1 minus 120590)

120590119872119904119903

119877119903 119901120596minus119877119903

120590119871119903

]]]]]]]]]

]

times

[[[[[

[

120593119904120572

120593119904120573

120593119903120572

120593119903120573

]]]]]

]

+

[[[[[

[

1 0

0 1

0 0

0 0

]]]]]

]

[V119904120572

V119904120573

]

[[[

[

119894119904120572

119894119904120573

119894119903120572

119894119903120573

]]]

]

=

[[[[[[[[[[[

[

1

1205901198711199040


120590119872119904119903

0

01

1205901198711199040


120590119872119904119903


120590119872119904119903

01

120590119871119903minus119901120596


120590119872119904119903

1199011205961

120590119871119903

]]]]]]]]]]]

]

times[[[

[

120593119904120572

120593119904120573

120593119903120572

120593119903120573

]]]

]

002 004 006 008 01 012 014 016 018 02

0

20

40

60

80

100

120

140



minus20

Time (s)

Wm

(rad

s)


002 004 006 008 01 012 014 016 018 02

0

10

20

30

40

50

IL-p

hA (A



Time (s)

minus10

minus20

minus30

minus40


[[[

[

119894119904120572

119894119904120573

120593119903120572

120593119903120573

]]]

]

119899+1

=[[[

[

11989211 11989212 11989213 11989214

11989221 11989222 11989223 11989224

11989231 11989232 11989233 11989234

11989241 11989242 11989243 11989244

]]]

]

times[[[

[

119894119904120572

119894119904120573

120593119903120572

120593119903120573

]]]

]

119899

+[[[

[

ℎ11 ℎ12

ℎ21 ℎ22

ℎ31 ℎ32

ℎ41 ℎ42

]]]

]

[119881119904120572

119881119904120573

]

119899

(18)

where 120590 = 1minus(1198722




002 004 006 008 01 012 014 016 018 02

0

50

100

150

EMF

phas

e A (V


EMF phase A RTDS

minus50

minus100

minus150

Time (s)




composerstudio


input

DSP1

DSP2


module-2

RTDS

DSP1

DSP2

UART


output



= 0 and 119894119904120573

= 0 Then119864119904120572

= 119881119904120572 119864119904120573

= 119881119904120573

[119864119904120572

119864119904120573

]

119899

=minus1


ℎ22 minusℎ12

minusℎ21 ℎ11]

times [11989213 11989214

11989223 11989224] [

120593119903120572

120593119903120573

]

119899

(19)

ePWM3

WAWB

C280xC28x3xePWM

ePWM2

WAWB

C280xC28x3x

ePWM

ePWM1

WA

WB

C280xC28x3x

ePWM

Sine wave3

Sine wave2

Sine wave1

F28335 eZdsp


Uint16


Uint16


Uint16




Ls = 10mH


119898 = 08

As given in Table 3

where g119898119899 h119898119899









10050

0minus50

minus100018 0185 019 0195 02 0205 021 0215 022 0225

Time (s)


Phas

e-ph

ase

volta

ge (V

)

2010

0minus10minus20


Inpu

t R-p

hase

curr

ent (

A)

018 0185 019 0195 02 0205 021 0215 022 0225Time (s)

(a)

80604020

002 0202 0204 0206 0208 021 0212 0214 0216 0218 022

Time (s)

DC

link

(V)

DC link voltage

201510

50

minus5

DC

link

curr

ent (

A)

02 0202 0204 0206 0208 021 0212 0214 0216 0218 022Time (s)

DC link current

(b)

105

0019 0195 02 0205 021 0215 022 0225 023 0235

Time (s)

Gat

e pul

se (V




019 0195 02 0205 021 0215 022 0225 023 0235Time (s)

019 0195 02 0205 021 0215 022 0225 023 0235Time (s)

Gat

e pul

se (V

)

105

0

105

0

Gat

e pul

se (V

)

(c)

10050

0minus50

minus10002 0205 021 0215 022 0225 023 0235 024 0245

Time (s)

AC output voltagePh

ase-

phas

evo

ltage

(V)

3210

minus1minus2minus3

R-ph

ase c

urre

nt (A


02 0205 021 0215 022 0225 023 0235 024 0245Time (s)

(d)





(119887)


1 DC link voltage V 001 8546 8588 04910102 5001 5009 01





6 Rotor speed 120596 (rads) 002 3141 3171 0901922 14848 14851 002


(a) (b)

(c) (d)








6 Conclusion









Appendices



B


References













RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













119889

119889119905119883 (119905) = [119860

119888(120596)] 119883 (119905) + [119861

119888] 119880 (119905)

119884 (119905) = [119862119888] 119883 (119905)

(17)


119888(120596)] [119861

119888] and [119862

119888] are state



119889

119889119905

[[[[[

[

120593119904120572

120593119904120573

120593119903120572

120593119903120573

]]]]]

]

=

[[[[[[[[[

[

minus119877119904

1205901198711199040

(1 minus 120590) 119877119904

120590119872119904119903

0

0minus119877119904

1205901198711199040

(1 minus 120590) 119877119904

120590119872119904119903

(1 minus 120590)

120590119872119904119903

119877119903 0minus119877119903

120590119871119903minus119901120596

0(1 minus 120590)

120590119872119904119903

119877119903 119901120596minus119877119903

120590119871119903

]]]]]]]]]

]

times

[[[[[

[

120593119904120572

120593119904120573

120593119903120572

120593119903120573

]]]]]

]

+

[[[[[

[

1 0

0 1

0 0

0 0

]]]]]

]

[V119904120572

V119904120573

]

[[[

[

119894119904120572

119894119904120573

119894119903120572

119894119903120573

]]]

]

=

[[[[[[[[[[[

[

1

1205901198711199040


120590119872119904119903

0

01

1205901198711199040


120590119872119904119903


120590119872119904119903

01

120590119871119903minus119901120596


120590119872119904119903

1199011205961

120590119871119903

]]]]]]]]]]]

]

times[[[

[

120593119904120572

120593119904120573

120593119903120572

120593119903120573

]]]

]

002 004 006 008 01 012 014 016 018 02

0

20

40

60

80

100

120

140



minus20

Time (s)

Wm

(rad

s)


002 004 006 008 01 012 014 016 018 02

0

10

20

30

40

50

IL-p

hA (A



Time (s)

minus10

minus20

minus30

minus40


[[[

[

119894119904120572

119894119904120573

120593119903120572

120593119903120573

]]]

]

119899+1

=[[[

[

11989211 11989212 11989213 11989214

11989221 11989222 11989223 11989224

11989231 11989232 11989233 11989234

11989241 11989242 11989243 11989244

]]]

]

times[[[

[

119894119904120572

119894119904120573

120593119903120572

120593119903120573

]]]

]

119899

+[[[

[

ℎ11 ℎ12

ℎ21 ℎ22

ℎ31 ℎ32

ℎ41 ℎ42

]]]

]

[119881119904120572

119881119904120573

]

119899

(18)

where 120590 = 1minus(1198722




002 004 006 008 01 012 014 016 018 02

0

50

100

150

EMF

phas

e A (V


EMF phase A RTDS

minus50

minus100

minus150

Time (s)




composerstudio


input

DSP1

DSP2


module-2

RTDS

DSP1

DSP2

UART


output



= 0 and 119894119904120573

= 0 Then119864119904120572

= 119881119904120572 119864119904120573

= 119881119904120573

[119864119904120572

119864119904120573

]

119899

=minus1


ℎ22 minusℎ12

minusℎ21 ℎ11]

times [11989213 11989214

11989223 11989224] [

120593119903120572

120593119903120573

]

119899

(19)

ePWM3

WAWB

C280xC28x3xePWM

ePWM2

WAWB

C280xC28x3x

ePWM

ePWM1

WA

WB

C280xC28x3x

ePWM

Sine wave3

Sine wave2

Sine wave1

F28335 eZdsp


Uint16


Uint16


Uint16




Ls = 10mH


119898 = 08

As given in Table 3

where g119898119899 h119898119899









10050

0minus50

minus100018 0185 019 0195 02 0205 021 0215 022 0225

Time (s)


Phas

e-ph

ase

volta

ge (V

)

2010

0minus10minus20


Inpu

t R-p

hase

curr

ent (

A)

018 0185 019 0195 02 0205 021 0215 022 0225Time (s)

(a)

80604020

002 0202 0204 0206 0208 021 0212 0214 0216 0218 022

Time (s)

DC

link

(V)

DC link voltage

201510

50

minus5

DC

link

curr

ent (

A)

02 0202 0204 0206 0208 021 0212 0214 0216 0218 022Time (s)

DC link current

(b)

105

0019 0195 02 0205 021 0215 022 0225 023 0235

Time (s)

Gat

e pul

se (V




019 0195 02 0205 021 0215 022 0225 023 0235Time (s)

019 0195 02 0205 021 0215 022 0225 023 0235Time (s)

Gat

e pul

se (V

)

105

0

105

0

Gat

e pul

se (V

)

(c)

10050

0minus50

minus10002 0205 021 0215 022 0225 023 0235 024 0245

Time (s)

AC output voltagePh

ase-

phas

evo

ltage

(V)

3210

minus1minus2minus3

R-ph

ase c

urre

nt (A


02 0205 021 0215 022 0225 023 0235 024 0245Time (s)

(d)





(119887)


1 DC link voltage V 001 8546 8588 04910102 5001 5009 01





6 Rotor speed 120596 (rads) 002 3141 3171 0901922 14848 14851 002


(a) (b)

(c) (d)








6 Conclusion









Appendices



B


References













RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










002 004 006 008 01 012 014 016 018 02

0

50

100

150

EMF

phas

e A (V


EMF phase A RTDS

minus50

minus100

minus150

Time (s)




composerstudio


input

DSP1

DSP2


module-2

RTDS

DSP1

DSP2

UART


output



= 0 and 119894119904120573

= 0 Then119864119904120572

= 119881119904120572 119864119904120573

= 119881119904120573

[119864119904120572

119864119904120573

]

119899

=minus1


ℎ22 minusℎ12

minusℎ21 ℎ11]

times [11989213 11989214

11989223 11989224] [

120593119903120572

120593119903120573

]

119899

(19)

ePWM3

WAWB

C280xC28x3xePWM

ePWM2

WAWB

C280xC28x3x

ePWM

ePWM1

WA

WB

C280xC28x3x

ePWM

Sine wave3

Sine wave2

Sine wave1

F28335 eZdsp


Uint16


Uint16


Uint16




Ls = 10mH


119898 = 08

As given in Table 3

where g119898119899 h119898119899









10050

0minus50

minus100018 0185 019 0195 02 0205 021 0215 022 0225

Time (s)


Phas

e-ph

ase

volta

ge (V

)

2010

0minus10minus20


Inpu

t R-p

hase

curr

ent (

A)

018 0185 019 0195 02 0205 021 0215 022 0225Time (s)

(a)

80604020

002 0202 0204 0206 0208 021 0212 0214 0216 0218 022

Time (s)

DC

link

(V)

DC link voltage

201510

50

minus5

DC

link

curr

ent (

A)

02 0202 0204 0206 0208 021 0212 0214 0216 0218 022Time (s)

DC link current

(b)

105

0019 0195 02 0205 021 0215 022 0225 023 0235

Time (s)

Gat

e pul

se (V




019 0195 02 0205 021 0215 022 0225 023 0235Time (s)

019 0195 02 0205 021 0215 022 0225 023 0235Time (s)

Gat

e pul

se (V

)

105

0

105

0

Gat

e pul

se (V

)

(c)

10050

0minus50

minus10002 0205 021 0215 022 0225 023 0235 024 0245

Time (s)

AC output voltagePh

ase-

phas

evo

ltage

(V)

3210

minus1minus2minus3

R-ph

ase c

urre

nt (A


02 0205 021 0215 022 0225 023 0235 024 0245Time (s)

(d)





(119887)


1 DC link voltage V 001 8546 8588 04910102 5001 5009 01





6 Rotor speed 120596 (rads) 002 3141 3171 0901922 14848 14851 002


(a) (b)

(c) (d)








6 Conclusion









Appendices



B


References













RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










10050

0minus50

minus100018 0185 019 0195 02 0205 021 0215 022 0225

Time (s)


Phas

e-ph

ase

volta

ge (V

)

2010

0minus10minus20


Inpu

t R-p

hase

curr

ent (

A)

018 0185 019 0195 02 0205 021 0215 022 0225Time (s)

(a)

80604020

002 0202 0204 0206 0208 021 0212 0214 0216 0218 022

Time (s)

DC

link

(V)

DC link voltage

201510

50

minus5

DC

link

curr

ent (

A)

02 0202 0204 0206 0208 021 0212 0214 0216 0218 022Time (s)

DC link current

(b)

105

0019 0195 02 0205 021 0215 022 0225 023 0235

Time (s)

Gat

e pul

se (V




019 0195 02 0205 021 0215 022 0225 023 0235Time (s)

019 0195 02 0205 021 0215 022 0225 023 0235Time (s)

Gat

e pul

se (V

)

105

0

105

0

Gat

e pul

se (V

)

(c)

10050

0minus50

minus10002 0205 021 0215 022 0225 023 0235 024 0245

Time (s)

AC output voltagePh

ase-

phas

evo

ltage

(V)

3210

minus1minus2minus3

R-ph

ase c

urre

nt (A


02 0205 021 0215 022 0225 023 0235 024 0245Time (s)

(d)





(119887)


1 DC link voltage V 001 8546 8588 04910102 5001 5009 01





6 Rotor speed 120596 (rads) 002 3141 3171 0901922 14848 14851 002


(a) (b)

(c) (d)








6 Conclusion









Appendices



B


References













RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a) (b)

(c) (d)








6 Conclusion









Appendices



B


References













RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















Appendices



B


References













RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article Development of a New Research Platform ...downloads.hindawi.com/journals/ape/2013/719847.pdf · Research Article Development of a New Research Platform for Electrical